Inversion of noisy Radon transform by SVD based needlets

Gérard Kerkyacharian; George Kyriazis; Erwan Le Pennec; Pencho Petrushev; Dominique Picard

doi:10.1016/j.acha.2009.06.001

Inversion of noisy Radon transform by SVD based needlets

Gérard Kerkyacharian
, George Kyriazis
, Erwan Le Pennec
, Pencho Petrushev
, Dominique Picard

Universite Paris Diderot
Laboratoire de Probabilités et Modèles Aléatoires

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

A linear method for inverting noisy observations of the Radon transform is developed based on decomposition systems (needlets) with rapidly decaying elements induced by the Radon transform SVD basis. Upper bounds of the risk of the estimator are established in L^p (1 ≤ p ≤ ∞) norms for functions with Besov space smoothness. A practical implementation of the method is given and several examples are discussed.

Original language	English
Pages (from-to)	24-45
Number of pages	22
Journal	Applied and Computational Harmonic Analysis
Volume	28
Issue number	1
DOIs	https://doi.org/10.1016/j.acha.2009.06.001
Publication status	Published - 1 Jan 2010
Externally published	Yes

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10.1016/j.acha.2009.06.001

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title = "Inversion of noisy Radon transform by SVD based needlets",

abstract = "A linear method for inverting noisy observations of the Radon transform is developed based on decomposition systems (needlets) with rapidly decaying elements induced by the Radon transform SVD basis. Upper bounds of the risk of the estimator are established in Lp (1 ≤ p ≤ ∞) norms for functions with Besov space smoothness. A practical implementation of the method is given and several examples are discussed.",

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AU - Kerkyacharian, Gérard

AU - Kyriazis, George

AU - Le Pennec, Erwan

AU - Petrushev, Pencho

AU - Picard, Dominique

PY - 2010/1/1

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AB - A linear method for inverting noisy observations of the Radon transform is developed based on decomposition systems (needlets) with rapidly decaying elements induced by the Radon transform SVD basis. Upper bounds of the risk of the estimator are established in Lp (1 ≤ p ≤ ∞) norms for functions with Besov space smoothness. A practical implementation of the method is given and several examples are discussed.

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DO - 10.1016/j.acha.2009.06.001

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AN - SCOPUS:70350723470

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SP - 24

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JO - Applied and Computational Harmonic Analysis

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IS - 1

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Inversion of noisy Radon transform by SVD based needlets

Abstract

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